a sensitivity analysis of the social vulnerability...

Risk Analysis, Vol. 28, No. 4, 2008 DOI: 10.1111/j.1539-6924.2008.01072.x

A Sensitivity Analysis of the Social Vulnerability Index

Mathew C. Schmidtlein,1 Roland C. Deutsch,2 Walter W. Piegorsch,3 and Susan L. Cutter1∗

The Social Vulnerability Index (SoVI), created by Cutter et al. (2003), examined the spatialpatterns of social vulnerability to natural hazards at the county level in the United States inorder to describe and understand the social burdens of risk. The purpose of this article isto examine the sensitivity of quantitative features underlying the SoVI approach to changesin its construction, the scale at which it is applied, the set of variables used, and to variousgeographic contexts. First, the SoVI was calculated for multiple aggregation levels in the Stateof South Carolina and with a subset of the original variables to determine the impact of scalarand variable changes on index construction. Second, to test the sensitivity of the algorithm tochanges in construction, and to determine if that sensitivity was constant in various geographiccontexts, census data were collected at a submetropolitan level for three study sites: Charleston,SC; Los Angeles, CA; and New Orleans, LA. Fifty-four unique variations of the SoVI werecalculated for each study area and evaluated using factorial analysis. These results were thencompared across study areas to evaluate the impact of changing geographic context. Whiledecreases in the scale of aggregation were found to result in decreases in the variance explainedby principal components analysis (PCA), and in increases in the variance of the resultingindex values, the subjective interpretations yielded from the SoVI remained fairly stable.The algorithm’s sensitivity to certain changes in index construction differed somewhat amongthe study areas. Understanding the impacts of changes in index construction and scale arecrucial in increasing user confidence in metrics designed to represent the extremely complexphenomenon of social vulnerability.

KEY WORDS: Hazards; principal components analysis; sensitivity analyses; social vulnerability

1. INTRODUCTION

The impact of Hurricane Katrina on the GulfCoast, and in New Orleans in particular, was perhapsthe most visible recent demonstration of the needfor an integrative vulnerability science approach tohazards research in the United States (Cutter, 2003).While the prehurricane evacuation from New Orleans

1 Hazards & Vulnerability Research Institute, Department of Ge-ography, University of South Carolina, Columbia, SC, USA.

2 Department of Mathematics & Statistics, The University of NorthCarolina at Greensboro, Greensboro, NC, USA.

3 BIO5 Institute, University of Arizona, Tucson, AZ, USA.∗ Address correspondence to Susan L. Cutter, Hazards & Vulner-

ability Research Institute, Department of Geography, Universityof South Carolina, Columbia, SC 29223, USA; tel: (803)-777-1590;fax: 803-777-4972; [email protected].

was judged by some to be a success when measuredby the volume of evacuees who were able to flee in ashort timeframe and over limited highways (Wolshonet al., 2006), it was a devastating failure for the so-cially vulnerable population that was unable to leave(Cutter & Emrich, 2006). It is estimated that some250,000 residents in New Orleans had no access topersonal vehicles; even if the regional buses had beenused in the evacuation, they could have accommo-dated less than 10% of this number in a single trip(Wolshon et al., 2005). And, these figures do not ad-dress special needs or institutionalized populations,which accounted for about 10% of the fatalities fromKatrina in New Orleans (Schmidlin, 2006). Theseproblems highlight the need to better integrate socialscience research concerning social vulnerability into

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1100 Schmidtlein et al.

emergency and risk management decision making.Such integration will allow planners to better iden-tify what and where problems exist before an eventoccurs, and provide insight as to what steps may beuseful in remedying them (Chakraborty et al., 2005).

Toward this end, one approach for identifyingthe locations of populations with high levels of socialvulnerability is the social vulnerability index (SoVI)(Cutter et al., 2003). SoVI can be used to effectivelyquantify variations in the relative levels of social vul-nerability over time and across space (Cutter & Finch,2008). Yet like other comparable indicators, it is dif-ficult to systematically assess its veracity. Because ofthe complex and multidimensional nature of factorscontributing to vulnerability, no variable has yet beenidentified against which to fully validate such indices.An alternative approach to assess the robustness ofthe index is to identify how changes in its construc-tion may lead to changes in the outcome. Factors thatmay have a large influence on the outcome of the in-dex include changes in the set of variables used for in-dex construction, differences in scale of analysis, andchanges in the subjective decisions made in the in-dex algorithm. When we have a greater understand-ing of the way the index responds to these changes,we can more confidently interpret and implement itsresults. The purpose of this article is to conduct suchan assessment. Three research questions are asked.First, what is the impact of changes in variable setand analytical scale on the index results? Next, howrobust is the SoVI to changes in its algorithmic ap-proach? Finally, is the index sensitive to the samechanges in its construction in various geographic set-tings? The first question will be answered by com-paring indices calculated with two different variablesets and at differing scales within the State of SouthCarolina. The final two questions will be answered byconstructing a set of social vulnerability indices calcu-lated over varying algorithmic criteria in three loca-tions: the Charleston-North Charleston MetropolitanStatistical Area (MSA) in South Carolina, in Los An-geles County, California, and finally in Orleans Parish,Louisiana.

2. SOCIAL VULNERABILITY

While hazards and disasters researchers have longunderstood that human decisions have an influenceon the outcome of hazard events (Kates, 1971; Mileti,1980), it has only been within the past decade or so thatvulnerability as an explicit concept has been broadlyrecognized (Wisner et al., 2004). Although multi-

ple definitions of vulnerability have been proposed(Cutter, 1996), here we define it as the likelihood ofsustaining losses from some actual or potential haz-ard event, as well as the ability to recover from thoselosses.

Contributions to vulnerability can be divided intotwo broad categories: exposure or biophysical vul-nerability, those characteristics of events and phys-ical contexts that influence the likelihood of lossesand ability of individuals or communities to recover;and susceptibility or social vulnerability, which inter-acts with exposure to either increase or decrease theeventual harm (Cutter, 1996). Hazards, risk, and dis-aster researchers in the past have focused primarilyon elements related to biophysical vulnerability, per-haps because they are relatively less complex thanthose related to social vulnerability. Social vulnerabil-ity provides greater insight into the manner in whichthe decisions we make as a society influence our differ-ential experience of hazard events. Social vulnerabil-ity stems from limited access to resources and politicalpower, social capital, beliefs and customs, physicallimitations of the population, and characteristics ofthe built environment such as building stock and age,and the type and density of infrastructure and life-lines (Cutter et al., 2003). Others authors have dis-cussed in much greater detail many of the importanttheoretical and conceptual aspects of social vulnera-bility and its measurements, which we only touch uponhere (Adger, 2006; Birkman, 2006;Turner et al., 2003;Wisner et al., 2004; Eakin & Luers, 2006).

The antecedents of current efforts to model so-cial vulnerability were derived from the social scienceresearch in the 1960s and 1970s on social indicatorsand quality-of-life indicators. Much of the researcheffort in the intervening years has addressed inter-national indicators of human development and theirrelationship to natural hazards, but often data are notavailable at a subnational level (Bohle et al., 1994).More recent examples of social vulnerability mod-eling have been based on limited representations ofthe social characteristics involved (Cutter et al., 2000;Wu et al., 2002; Wood & Good, 2004; Chakrabortyet al., 2005), considered only particular aspects of vul-nerability (Luers et al., 2003), or focused on novelmethodological approaches for one specific case study(Rashed & Weeks, 2003; Inter-American Develop-ment Bank, 2006)

The social vulnerability modeling approach thatwe assess in this article, SoVI (Cutter et al., 2003),was developed to address many of these shortcom-ings. It originally was applied as an analysis of social

A Sensitivity Analysis of the Social Vulnerability Index 1101

contributions to natural hazard or disaster vulnerabil-ity at the county level in the United States for 1990. Itwas created by first finding social characteristics con-sistently identified within the research literature ascontributing to vulnerability. These target variableswere used to identify a set of 42 normalized inde-pendent variables that influenced vulnerability. The42 variables were then entered into a principal com-ponents analysis (PCA) (Manly, 2005), from which 11components were selected, explaining a total of 76.4%of the variance in the original data set.

These components were interpreted to identifywhat element of vulnerability they represented, andscaled to ensure that they contributed to the final in-dex in an appropriate manner (positive values addedto vulnerability, negative to mitigated vulnerability).The 11 factors were then summed with equal weightsto create the final vulnerability index. The index wasmapped, with counties shaded according to the SoVIvalues, to allow for identification of the spatial pat-terns of social vulnerability within the United States.A similar factor-analysis-based approach to charac-terizing social contributions to vulnerability was alsoused by Clark et al. (1998), who used a smaller enu-meration unit (census block group) for one particularstudy area (Revere, MA).

The SoVI approach has been replicated in a num-ber of studies in various geographic settings (Boruff& Cutter, 2007), at various spatial scales (Cutter et al.,2006; Borden et al., 2007), and in differing time peri-ods (Cutter & Emrich, 2006; Cutter & Finch, 2008).Indeed, the method may be best viewed as an algo-rithm for quantifying social vulnerability, rather thanas a simple numerical index. Via these approaches,SoVI has consistently illustrated its value by revealingboth anticipated and unanticipated spatial patternsthat conform to expert interpretations of social vul-nerability. But no study to date, including the originalSoVI article, has included a sensitivity analysis of theunderlying PCA-based approach.

3. STUDY AREA AND SCALE

The analysis was conducted in three separatestudy areas: Charleston, South Carolina; Los An-geles, California; and New Orleans, Louisiana. Toaddress changes in vulnerability across these loca-tions, we operate at the U.S. census tract level. ForCharleston, South Carolina, social vulnerability wascalculated within the Charleston-North CharlestonMSA, consisting of Charleston, Dorchester, andBerkeley Counties, South Carolina. Because of themuch larger number of census tracts within the Los

Angeles, California metropolitan area, the analysiswas carried out only for Los Angeles County. Or-leans Parish, Louisiana was used to represent the NewOrleans study area.

While the SoVI algorithm has been applied atmultiple scales in the existing literature, as notedabove, there has been no explicit consideration of theimpact scalar changes have on the analysis, beyondthe simple visual interpretations of patterns of vul-nerability. Because this analysis was conducted at thetract level, rather than at the county level as in theoriginal SoVI index, it is important to consider howthis change in scale may impact the analysis. Open-shaw (1983) identified two types of problems that canoccur as part of the modifiable areal unit problemwhen working with areally aggregated data at differ-ent scales. The first issue, termed the scale problem,is related to the ecological fallacy. As scales of analy-sis change, the relationships between variables aggre-gated to those levels may also change. Thus withoutaccess to the original, unaggregated data, it is impossi-ble to determine how severe this problem is, althoughseveral studies indicate that correlations tend to in-crease with increasing scales (Clark & Avery, 1976;Openshaw, 1983). This provides a fundamental chal-lenge to characterizing vulnerability at aggregatedlevels. The majority of existing research on social con-tributions to vulnerability has been conducted at ahousehold or individual level (Heinz Center, 2002).This body of work was used by Cutter et al. (2003) toidentify the characteristics that would be used to rep-resent vulnerability for populations within particulargeographic areas. While this approach seems reason-able, it is important to note that the ecological fallacymeans that variables that are influential to the vul-nerability of individuals or households may not havethe same level or type of relationship when examin-ing vulnerability of populations or groups. Addition-ally, SoVI as an areal measure of vulnerability appliesonly to the aggregate area as a whole, and does notrepresent individually based levels of vulnerability.This limitation of the ecological fallacy will remainas a challenge to all census- or demographic-basedapproaches to characterizing vulnerability until therelationships between particular areal descriptors forgroups (i.e., percentage of population in poverty) andindividual vulnerability have been determined.

To assess the impact of changes in scale betweenaggregation levels, Clark and Avery (1976) used anapproach in which the correlations between variableswere calculated for the same data and study areaat multiple scales. While this did not give insightinto the extent of the problem created by the initial


aggregation of observation units, it did provide amethod to assess the impact of the ecological fallacyon subsequent changes in aggregation scales. Combin-ing the assessment of changing scales with an explicitlimitation of the application of analytical results tothe scale at which they were derived provides a sim-ple means of addressing the impact of the scale issueon calculating SoVI at various aggregation levels. Theproblem then becomes one of choosing an appropri-ate scale of analysis. In this study, the desire was toaddress changes in vulnerability across a metropoli-tan area, so census tracts seem an appropriate level.The impact of scalar changes from the county to thetract level of aggregation was examined using an ap-proach based on Clark and Avery’s (1976) analysis,with South Carolina as the study area.

The second issue, termed by Openshaw to bethe aggregation problem, is that the relationships be-tween areally aggregated variables may result as muchfrom the aggregation scheme as from the fundamentalrelationships between the variables themselves. In-deed, dramatic differences in correlations betweenvariables may be produced by changing the aggre-gation scheme (Openshaw, 1983). This forces one toapply results from analyses of areal data only to thestudy units at which they were conducted. Short ofcreating new aggregation units, the problem here be-comes one of determining whether the study unitsused in an analysis are truly meaningful.

While it would be naı̈ve to view any preexist-ing areal aggregation as ideal for a given study, cen-sus tracts do seem to be a fairly meaningful spa-tial unit for our analysis. Tracts are defined by theU.S. Census Bureau in conjunction with local com-mittees of census data users, and are meant to repre-sent areas with fairly stable population sizes and tobe “relatively homogeneous . . . with respect to pop-ulation characteristics, economic status, and livingconditions” (U.S. Department of Commerce Bureauof the Census, 2006). Additionally, it has been ob-served that while not complete, census tracts haveprovided a relevant proxy for neighborhoods withinurban areas (Sampson et al., 2002). Census tractstherefore seem to be a pertinent set of spatial unitsfor modeling social vulnerability at the suburbanlevel.

4. DATA

The list of variables from the original SoVI, cre-ated using 1990 census variables, was used to guidethe selection of variables for our analysis. Changes

in census variable availability at the county and tractlevel necessitated that a smaller set of variables beused here. Additionally, following the approach takenby Borden et al. (2007), built environment variableswere removed from the analysis to focus more explic-itly on those characteristics of the populations thatthemselves contributed to vulnerability. This resultedin a total of 26 variables obtained from the GeoLyt-ics Neighborhood Change Database and U.S. Censusdata sources (GeoLytics, 2006; U.S. Department ofCommerce Bureau of the Census, 2002), shown inTable I.

5. SOVI ALGORITHM

The algorithm used to construct indices of vul-nerability in this article follows that used by Cutteret al. (2003), with the inclusion of data standardiza-tion for the input variables and the final index scores.The computations are carried out using the followingsteps:

1. Standardize all input variables to z-scores,each with mean 0 and standard deviation 1.

2. Perform the PCA with the standardized inputvariables.

3. Select the number of components to be furtherused based on the unrotated solution.

4. If desired, rotate the initial PCA solution.5. Interpret the resulting components on how

they may influence the social vulnerability andassign signs to the components accordingly.For this step, an output of the loadings ofeach variable on each factor was used to de-termine if high levels of a given factor tend toincrease or decrease social vulnerability. If afactor tends to show high levels for low socialvulnerability (e.g., wealth variable is stronglypositive), the corresponding factor scores aremultiplied by –1. In some cases, both high andlow levels may increase social vulnerability(e.g., elderly is strongly negative and childrenis strongly positive) and in this case the abso-lute value of the corresponding factor scorewas used for calculating SoVI. Adjustmentswere made to the sign of components ratherthan to the signs of variables at the outset be-cause of the a priori unpredictability of the di-rection of the relationships between the vari-ables and the components: variables whosesigns were adjusted prior to inclusion in thePCA may still load in a manner that indicates


Table I. Social Vulnerability Variables for Charleston, SC; Orleans, LA; and Los Angeles, CA study areas∗

Civilian labor force participation Percentage of female participation in civilian labor forceAverage family income Percentage of female-headed householdsMedian dollar value of owner occupied housing units Percentage of Native American population (American Indian,

Eskimo, or Aleut)Median gross rent ($) for renter-occupied housing units Percentage of population under 5 yearsPercentage of population who are immigrants Percentage of population 65 years or olderPercentage of institutionalized elderly population Percentage of living in povertyAverage number of people per household Percentage of renter occupied housing unitsPercentage of employed in primary industry: farming, fishing,

mining, forestryPercentage of rural farm population

Percentage of Asian or Pacific Islander Percentage of Hispanic personsPercentage of black population Percentage employed in transportation, communications, and other

public utilitiesPercentage of the civilian labor force unemployed Percentage of the population living in urban areasPercentage of population over 25 years old with less than 12 years

of educationPercentage employed in service occupations

Percentage of females Percentage of households that receive Social Security benefits

∗The variables deleted from the subcounty analysis but that appeared in the original SoVI include variables relating to the built environment(percentage of housing units that are mobile homes, per capita community hospitals, number of housing units per square mile, number ofhousing permits per new residential construction per square mile, number of manufacturing establishments per square mile, earnings inall industries per square mile, number of commercial establishments per square mile, and value of all property and farm products sold persquare mile) and social variables unavailable or less meaningful at the tract level for our study areas (median age, general local governmentdebt to revenue ratio, number of physicians per 100,000 population, percentage of votes cast for winning presidential candidate in mostrecent election, birth rate, land in farms as a percentage of total land, percentage population change in last decade, percentage of householdsearning more than $75,000).

that the component would decrease vulnera-bility, and so adjusting the sign of variablesbefore entry into the PCA would not have re-moved the need for this step.

6. Combine the selected component scores intoa univariate score using a predeterminedweighting scheme.

7. Standardize the resulting scores to mean 0 andstandard deviation 1.

Because PCA is sensitive to the values of the in-put variables, the data standardization step is highlyrecommended, allowing all variables to have the samemagnitude. With the standardized data set the PCAcan be performed in the second step. It returns a set oforthogonal components that are the linear combina-tions of the original variables. By construction the firstcomponent is the linear combination that explains thegreatest variations among the original variables, thesecond (orthogonal) component the greatest remain-ing variation, and so on. Based on the results of theperformed PCA, it is desirable to select a parsimo-nious subset of components that explains the under-lying features in the data as closely as possible: inthe work of Cutter et al. (2003), the Kaiser criterionwas used to select parsimonious components (Step

3). Also, a varimax rotation was used (Step 4), andthe interpreted components were summed with equalweights (Step 6).

Our sensitivity analysis for this algorithm is con-ducted in two main stages: first, a consideration ofthe sensitivity to minor changes in variables used andthe scale at which the analysis was applied, and sec-ondly, the sensitivity to changes in the manner of in-dex construction. For the sake of simplicity, the meth-ods and results for these two stages will be presentedtogether.

6. TEST 1: VARIABLE SET AND SCALECHANGES

The first sensitivity test examined the role ofdownscaling and that of operating with a reducedvariable set on SoVI construction. The first analyticalstep determined the impact of these two differences(scale and variable set) on the constructed indices us-ing the subset of variables collected at the census tractlevel for the entire State of South Carolina. To deter-mine the impact of using the subset of variables, thesedata then were aggregated to the county level. TwoSoVIs were calculated at the county level, the firstwith the 33 social vulnerability variables used in the


Table II. County-Level Index Comparison

Original Social Variables (N = 33) Subset Social Variables (N = 26)

# Components selected 8 6Pct. variance explained (6 components) 74.8 85.0Pct. variance explained (8 components) 85.8 91.2Component interpretation (pct. variance explained) 1. Wealth (22.2) 1. Wealth (29.5)

2. Race & poverty (20.2) 2. Race & poverty (21.8)3. Age (elderly) (13.8) 3. Hispanic immigrants (10.8)4. Hispanic immigrants (6.7) 4. Age (9.3)5. Age (children) (6.1) 5. Gender (7.7)6. Infrastructure employment (6.0) 6. Race (6.1)7. Gender & nursing homes (5.9)8. Community debt load (5.1)

original SoVI, and the second with the 26 variablesused instead in the tract-level analysis. The algorithmemployed in this stage of the analysis followed the ap-proach of Cutter et al. (2003), using the Kaiser crite-rion for component selection, a varimax rotation, andequal weighting to sum the collected components.

6.1. Variable Set Results

Strong similarities were found between the twoindices. The PCA performed on the original set of 33social variables led to selection of eight components,which explained 85.8 % of the variance of the originaldata (Table II). The PCA performed on the subset of26 variables led to 6 components, explaining 85.0%of the data variance. The set of components derivedfrom both PCAs had broadly similar subject interpre-tations.

The Spearman’s rank order correlation betweenthe two indices showed a fairly strong positive re-lationship (rs = 0.71; p < 0.01). The average rankchange between the two indices was 7, or about 16%of the total number of counties. All three of the coun-ties identified as the highest vulnerability group (withz-scores greater than or equal to 1.5) via the originalapproach also exceeded this level in the 26-variableapproach. Two additional counties were identified inthis highest vulnerability category via the 26-variableapproach, one of which was in the next lower vulner-ability group (z-scores from 0.5 to 1.5), and the otherfrom the medium vulnerability group (z-scores from−0.5 to 0.5). Overall, only 12 of the 42 counties hadrank changes of 10 or greater, and only two countiesexperienced changes in values great enough to movethem from lower to higher, or higher to lower, vulner-ability status.

6.2. Scale Results

The impact of changing the level of aggregationon the analysis was assessed via the approach used byClark and Avery (1976). These authors demonstratedthat as the level of aggregation increases, the correla-tions between variables increase as well. Because theSoVI approach is based on PCA, which itself relies onthe correlations between variables to determine thecomponents representing the maximum dimensionsof variability in the data set, it seems reasonable tosuspect that decreasing the level of aggregation fromthe county level—the aggregation scale used in Cutteret al.’s (2003) original work—to the tract level wouldresult in a decrease in the amount of variance ex-plained by the PCA used to construct the index. Toassess this, as well as to determine any other effectsof downscaling the SoVI approach, social vulnerabil-ity indices were constructed at the county and tractlevels for the State of South Carolina, as well as at amanually created intermediate level of aggregation.Four of the counties in the state had only three tracts,meaning that no intermediate aggregation could becreated that would result in a set of units completelyunique from the tract and county levels of aggrega-tion. As such, these counties were removed from thisanalysis, as well as from the previous comparison ofindices at the county level.

The results of the PCAs conducted at multiple ag-gregation scales are shown in Table III. As expected,as the level of aggregation at which the PCA was con-ducted decreased, the variance explained decreased,and the number of components selected using theKaiser criterion increased. Fig. 1 shows a graph of thepercentage of variance explained by the rotated com-ponents selected for each PCA. From this graph, wecan see that decreasing the level of aggregation tendsto flatten the displayed curve, meaning that both the


Table III. Results for County, Intermediate, and Tract Level PCAs

County Level Intermediate Level Tract Level

# Components 6 6 7Pct. variance explained 85.0 79.3 73.2Unstandardized index variance 4.45 5.09 6.66Unstandardized index range 10.38 11.33 29.25Component interpretation 1. Urban wealth 1. Race & poverty 1. Race & poverty

(pct. variance explained) (29.5) (22.6) (17.6)2. Race & poverty 2. Urban renters 2. Rural/urban

(21.8) (16.3) (11.7)3. Hispanic immigrants (10.8) 3. Wealth (13.6) 3. Wealth (10.9)4. Age (9.3) 4. Age (11.3) 4. Age (elderly) (9.6)5. Gender (7.7.) 5. Hispanic immigrants (8.6) 5. Hispanic immigrants (8.8)6. Race (6.1) 6. Gender (6.9) 6. Age (kids)

7. Gendered labor (6.8)

Fig. 1. Variance explained bycomponent for three aggregationlevels.

variance explained by the first rotated component isdecreased, and the rate of decrease in variance ex-plained is also reduced. Returning to Table III, wesee that while there are differences among the sub-ject interpretation of the components between thescales, they are broadly similar. The table also indi-cates that as the aggregation scale decreased, the vari-ance and range of the unstandardized indices com-puted from the PCAs increased. Finally, Fig. 2 showsthat the representations of vulnerability at the multi-ple levels of aggregation seem fairly stable; high vul-nerability counties are composed of moderate andhigh vulnerability tracts, while low vulnerability coun-ties are composed of moderate and low vulnerabilitytracts.

7. TEST 2: INDEX CONSTRUCTION CHANGES

The second step in our sensitivity analysis consid-ered the influence of subjective options applied in theconstruction of the index. The algorithm used for con-structing the original SoVI was reviewed to identifythe types of subjective decisions made that seemedlikely to have some influence on the assignment ofindex values. These fell into three categories: PCAcomponent selection (Step 3), PCA rotation (Step4), and the weighting scheme used to combine thecomponents to create the final index (Step 6). Logicalalternatives to each of these approaches were con-sidered, and index values for each study area werecalculated based on all possible combinations of them.


Fig. 2. Social vulnerability index value for multiple aggregation levels in South Carolina.

This approach resulted in a collection of indices forthe Charleston, Los Angeles, and Orleans study ar-eas. The values of the index could then be comparedbetween study areas to determine if the results of theanalysis remained stable across a variety of regionallocations.

Within each of the three different categories forindex construction, a number of options were con-sidered. The following methods for PCA compo-nent selection were studied for calculating the SoVIindex:

1. Kaiser criterion (Kaiser, 1960): Select onlythose components whose eigenvalues aregreater than one.

2. Percentage variance explained: Retain asmany components as needed in order to ac-count for a prespecified amount of variationin the original data. For the SoVI algorithm,the fewest number of components were cho-sen such that at least 80% of the variation inthe original data was accounted for.

3. Horn’s parallel analysis (Horn, 1958): Thisselection criterion is similar to the Kaisercriterion. However, instead of using a fixedthreshold one retains those factors whose

eigenvalues are larger than the expectedeigenvalue for that component. As the ex-pected eigenvalue is arduous to compute,Horn’s parallel analysis uses 100 randomlygenerated data sets on which a PCA is per-formed and then averages over the resultingeigenvalues.

4. Expert choice: Another approach for selectingcomponents relies upon subjectively identify-ing a set of components that have meaningful,subject area interpretations. We term this se-lection criteria “expert choice.”

A total of six PCA rotation methods wereconsidered:

1. Unrotated solution: In order to use the com-ponents that explain the greatest percentageof the original variation, no rotation is applied.

2. Varimax rotation (Kaiser, 1958): This rotationtends to load each variable highly on just onecomponent. This often leads to easier compo-nent interpretation.

3. Quartimax rotation (Neuhaus, 1954; Carroll,1953; Ferguson, 1954; Saunders, 1953): Thisrotation tends to increase large loadings anddecrease small ones, so that each variable will


load only on a few factors. This should leadto fewer relevant components than other ro-tations.

4. Promax rotation (Hendrickson & White,1964): In contrast to the other rotations, thepromax rotation represents an oblique rota-tion. Thus, the rotated components are nolonger orthogonal. By allowing the resultingcomponents to be correlated with each other,one may hope to achieve even easier inter-pretability. The promax rotation also requiresspecification of a power parameter, which istypically taken between 2 and 4. We chose thevalues 2, 3, and 4 for the algorithm.

Lastly, three approaches for weighting the se-lected and interpreted components were considered:

1. Sum the component scores: Since each PCAcomponent absorbs a different aspect of socialvulnerability a simple approach of combin-ing the components is to sum the scores, thusassigning equal contributions to each compo-nent of the SoVI value.

2. First component only: Mathematically, thefirst extracted component from a PCA is thelinear combination that explains the largestamount of variation in the original data.Therefore, selecting just the first componentwill give the mathematically optimal value tosummarize all the input variables in a singlecombination.

3. Weighted sum using explainable variance toweigh each component: This is a compromisebetween the first two methods. Since each suc-cessive component contributes progressivelyless to the explainable variation, it seems rea-sonable to give the first PCA component themost weight and to decrease the weights ac-cordingly for the remaining components. Thuswe chose a weighting scheme where each com-ponent’s weight was taken as the proportionof total variation that particular componentexplains.

In total, 72 different versions of social vulnera-bility indices were possible for each study area. Inthe end, only 54 unique versions were calculated be-cause the expert choice component selection alwayscoincided with the Kaiser criteria selection, and wastherefore dropped from the analysis. The approachfor this segment of the analysis was implemented us-ing SAS Software (SAS Institute Inc., 2004).

Finally, since the computed SoVI value does notitself have any absolute interpretation, it is standard-ized to a z-score with mean 0 and variance 1 in orderto map the values over space or to compare differ-ent methods. Positive values suggest high social vul-nerability, whereas negative values suggest low socialvulnerability. We considered these tracts with z-scorevalues greater than 1.5 as being highly vulnerable, andthose with values between 0.5 and 1.5 as having mod-erately high vulnerability. Tracts with values between−0.5 and 0.5 were considered as having moderate vul-nerability. Similar, but negative ranges were used toidentify moderately low and low vulnerability tracts.

7.1. Methods

To determine the impact of these subjective op-tions on the final index values, we statistically assessedchanges in SoVI using a three-way factorial analysis ofthe component selection, PCA rotation, and weight-ing scheme options. In this setting, we also accountedfor the census tract by viewing the tract ID within eachstudy area as a blocking factor, that is, an explanatoryvariable where tract ID represents a known sourceof variability. This helps to reduce residual variationand improve precision in the factorial analysis. Be-cause the computed index values do not represent atruly random sample drawn from some broader pop-ulation, this operation is not intended to make anystatistical inferences. Rather, we use this calculationsimply to reveal if substantial differences in the indexvalues within each study area occurred as a result ofthe choice(s) of subjective option.

In the factorial analysis, we employed partial(“Type III”) sums of squares to assess the impor-tance of each subjective option. The associated p-values were treated as measures of the influence eachsubjective option has on the final index value. Smallp-values suggest that changes in the choice of thatsubjective option have a large impact on the final in-dex value, whereas large p-values suggest that choiceswithin that subjective option do not substantially im-pact the final value.

For additional guidance on how changes in eachspecific option affected the final index values, we fur-ther assessed differences among the levels within eachsubjective option, using multiple comparison tech-niques. This was done using the all-possible-pairwisefamily of multiple comparisons: all possible paired dif-ferences were examined via Tukey’s method (Tukey,1994) to ensure proper multiplicity adjustment forthe family of paired comparisons. Here, a difference


between two choices of a subjective option that ex-hibits a small p-value suggests that changing from onechoice of the option to the other produces quite dif-ferent final index values, whereas a p-value close to1 suggests no substantial difference in how the twochoices for the option affect the final index value.

7.2. Results

Results from the factorial analysis illustrate theimpact of changes in the algorithm construction onthe index values for each study area. In this anal-ysis, p-values less than 0.10 were taken to indicatesubstantial differences in index construction resultingfrom a particular set of subjective decisions (selec-tion, rotation, and combination), or in the case of themultiplicity-adjusted results, differences between theoptions within a set. Table IV begins with the TypeIII sum of squares (SS) from the factorial analysisof the Charleston-North Charleston area. The tablealso includes Type III SS results for the tract ID con-tribution. Since ID is being employed as a blockingvariable to account for the known source of variabil-ity that it represents, the analysis of those p-valuesis irrelevant. They are only included in the table forcompleteness. Next, in Table IV, we see componentselection and combination method both result in sub-stantial changes in the SoVI score for Charleston.Rotation method shows little variation. Table V andTable VI show the multiplicity-adjusted results for the

Table IV. Factorial Analysis Results for All Study Sites∗

Type III Mean FSource DF SS Square Value Pr > F∗

Charleston-North Charleston

ID 116 2171.35 18.72 28.19 <0.0001Select 2 4.90 2.45 3.69 0.02Rotate 5 0.52 0.10 0.16 0.98Combine 2 29.34 14.67 22.10 <0.0001

Los Angeles

ID 2046 45312.29 22.15 37.40 <0.0001Select 2 0.20 0.10 0.16 0.85Rotate 5 50.63 10.13 17.10 <0.0001Combine 2 96.80 48.40 81.73 <0.0001

New Orleans

ID 180 3424.32 19.02 31.32 <0.0001Select 2 4.21 2.11 3.46 0.03Rotate 5 6.92 1.38 2.27 0.04Combine 2 79.25 39.63 65.10 <0.0001

∗Bold p values (less than 0.10) indicate substantial differences inindex construction.

Table V. P-Values for Pairwise Differences in ComponentSelection for All Study Sites∗

VarianceHorn Kaiser Explained

Charleston-North CharlestonHorn 0.02 0.12Kaiser 0.02 0.80Variance explained 0.12 0.80

Los Angeles

Horn 0.85 0.90Kaiser 0.85 0.99Variance explained 0.90 0.99

New Orleans

Horn 0.12 0.74Kaiser 0.12 0.04Variance explained 0.74 0.04


options within each of these categories. The Horn andKaiser selection criteria appear to differ substantiallyfor Charleston, while lesser differences occur betweenthe other selection criteria (Table V). For componentcombination, the weighted sum approach appears todiffer substantially from the other two approaches(Table VI).

Table IV next presents the Type III SS analysisfor index values in Los Angeles. Here, SoVI scoresare influenced by changes in the PCA componentcombination and rotation criteria. As was the casein the Charleston-North Charleston study area, the

Table VI. P-Values for Pairwise Differences in FactorCombination for All Study Sites∗

First WeightedFactor Sum Sum

Charleston-North CharlestonFirst factor 0.26 <0.0001Sum 0.26 <0.0001Weighted sum <0.0001 <0.0001

Los Angeles

First factor 0.16 <0.0001Sum 0.16 <0.0001Weighted sum <0.0001 <0.0001

New Orleans

First factor 1.00 <0.0001Sum 1.00 <0.0001Weighted sum <0.0001 <0.0001



Table VII. P-Values for PairwiseDifferences in Factor Rotation for All

Study Sites∗

Unrotated Varimax Quartimax Promax 2 Promax 3 Promax 4

Charleston-North CharlestonUnrotated 1.00 1.00 1.00 1.00 1.00Varimax 1.00 1.00 1.00 0.99 0.99Quartimax 1.00 1.00 1.00 0.99 0.99Promax 2 1.00 1.00 1.00 1.00 0.99Promax 3 1.00 0.99 0.99 1.00 1.00Promax 4 1.00 0.99 0.99 0.99 1.00

Los Angeles

Unrotated <0.0001 <0.0001 <0.0001 <0.0001 <0.0001Varimax <0.0001 1.00 1.00 0.08 0.51Quartimax <0.0001 1.00 1.00 0.08 0.51Promax 2 <0.0001 1.00 1.00 0.08 0.51Promax 3 <0.0001 0.08 0.08 0.08 0.95Promax 4 <0.0001 0.51 0.51 0.51 0.95

New Orleans

Unrotated 0.89 0.85 1.00 0.18 0.93Varimax 0.89 1.00 0.99 0.93 0.40Quartimax 0.85 1.00 0.98 0.85 0.35Promax 2 1.00 0.99 0.98 0.44 0.73Promax 3 0.18 0.93 0.85 0.44 0.03Promax 4 0.93 0.40 0.35 0.73 0.03

∗Bold p values (less than 0.10) indicate substantial differences in index construction.

weighted sum combination approach appears sub-stantially different from both of the other combina-tion approaches (Table VI). Since rotation appearsinfluential for the Los Angeles study area, we refer tomultiplicity-adjusted results in Table VII, where theunrotated approaches appear substantially differentfrom all other rotations, and the promax (k = 3) ro-tation appears different from all but the promax (k =4) rotation.

Finally, all three subjective decision categories ap-pear influential for Orleans Parish (Table IV). TheKaiser selection criterion appears substantially dif-ferent from the variance explained approach, andalso modestly different from the Horn selection cri-terion (Table V). As in Charleston-North Charlestonand Los Angeles, the weighted sum combination ap-proach appears substantially different from the othertwo approaches (Table VI). Lastly, the only substan-tial difference found in the rotation category was be-tween the promax (k = 3) and promax (k = 4) rota-tions (Table VII).

To understand the impact of these changes onthe relative rankings of individual tracts in each studyarea, rank changes were calculated between the vul-nerability index constructed following the originalSoVI approach (Kaiser selection, varimax rotation,and sum combination) and the remaining 53 index

construction approaches for each study area. His-tograms of these values for each study area, shownin Fig. 3, reveal that between 36–46% of the time,depending on study area, tracts experienced rankchanges corresponding to 10% or less of the to-tal range. In each study area, however, some rankchanges did occur, which were large enough to movetracts from the highest to the lowest category of vul-nerability.

8. DISCUSSION AND CONCLUSIONS

Based on these results, it is possible to reach ageneral set of conclusions regarding the sensitivity ofthe SoVI. The first question addresses the adequacy ofthe subset of variables used in the present sensitivityanalysis, and the impact of scalar changes on the PCAand resulting index. We find that the employed subsetof variables provided a representation of vulnerabil-ity with adequate similarity to that derived using thefull set of social variables employed in the originalSoVI, and that both approaches identify a similar setof highly vulnerable study units. With regard to theimpact of scalar changes on the analysis, our ability toexplain the variability in the data through the use ofPCA decreases with decreasing levels of aggregation,but the index values themselves become more spread


Fig. 3. Frequencies of the magnitude of rank changes. The rank changes are compared between the Kaiser criterion, varimax rotation, andsum component combination index (the original SoVI construction) and the remaining 53 variants. To allow for a more direct comparisonbetween study areas, vertical-axis units are the percentage of total rank changes, and horizontal-axis units are rank changes as a percentageof the total number of tracts for the study area.

out. Additionally, the subjective interpretations of thePCA components remained fairly stable across scales.This suggests that while scalar changes affect the PCAanalysis and the numeric properties of the index, theidentification of the drivers of vulnerability within astudy area, based on a constant variable set, are notstrongly dependent on the scale of aggregation usedto define the study area. Overall, the SoVI algorithmseems fairly robust to minor changes in variable se-lection, as well as to changes in the scale at which itis applied, especially downscaling from the county tocensus tract level.

While the performance of the SoVI algorithmdoes not appear to be substantially influenced byscalar changes or, more precisely, to changes in thelevel of aggregation to which it is applied, it is sensi-tive to variations in its construction. Representationsof vulnerability may be substantially different basedon the decisions made in index construction, includingdifferences in the sets of tracts in the highest vulnera-bility group. The algorithm is also sensitive to changesin study area location, suggesting that the geographiccontext in which the analysis is performed has an im-portant impact on the behavior of the index. In otherwords, places matter. This comes as no surprise as wewould expect variation in the results from study areato study area because local places are different in theirsocial characteristics and how they map onto the land-scape. There are, however, some general conclusionsthat can be drawn from our analyses. First, the onlyprocedure that had a substantial impact in all threestudy areas was the manner in which the componentswere combined to create the final index values. For

all three study areas, the variance weighted approachwas substantially different from the first componentonly and equal weights approaches. Second, when theselection criteria were important, the Kaiser criterionappeared substantially different from at least one ofthe others. Finally, there was no predictable pattern tothe impact of the rotation methods across study areas.

What implications does this sensitivity to changesin index construction have on future attempts to cre-ate vulnerability indices? The effect of changes in in-dex construction on the representation of vulnerabil-ity requires some method for assessing the validity ofthese representations, and then visualizing with maps.At present, the adequacy of the representation of vul-nerability produced by the index and visualization inmaps can only be determined by local expert knowl-edge of an area. For example, Fig. 4 and Fig. 5 showvulnerability maps for each study area using differ-ent selection criteria. The results appear quite differ-ent from one another, and without local knowledgeit is unclear which map is more accurate. Local ge-ographic knowledge of the areas suggests that Fig.4 (constructed with the original approach of Kaiserselection, varimax rotation, and equal weighted sum-ming of the components) is a closer approximationthan Fig. 5 to real-world patterns found in the cities.Applications of the SoVI algorithm using the originalSoVI approach have produced good results based onlocal knowledge of the study areas (Cutter & Finch,2008; Piegorsch et al., 2007; Borden et al., 2007; Boruff& Cutter, 2007; Cutter et al., 2006; Boruff et al., 2005).Nonetheless, in light of the sensitivity of the algo-rithm to changes in its construction, applications of


Fig. 4. SoVI values, constructed according to the original approach, using Kaiser criterion, varimax rotation, and sum component combina-tion.

Fig. 5. SoVI values, constructed using Horn’s parallel analysis, unrotated solution, and weighted sum component combination.


the SoVI should proceed cautiously and be coupledwith expert guidance to ensure that the representa-tions of vulnerability produced are reasonable andconsistent with locally based geographic knowledgeof the study area. The importance of expert judgmentin the index creation process is not limited to valida-tion of vulnerability representation. Expert judgmentis also a critical element in the subjective interpreta-tion of the components generated by the PCA (Step5 of the algorithm). These components must be in-terpreted to determine whether they are assigned apositive, negative, or absolute value before they arecombined to create the index. Future research on theSoVI algorithm could be designed to assess the im-pact of changes in the interpretation of componentson the final index and provide more concrete guid-ance to this crucial element. Perhaps the same set ofPCA components could be shown to a panel of localexperts, and the consistency of their judgments couldbe measured. Input from such a panel also would bebeneficial in determining not just the sensitivity of thealgorithm to changes in the subjective decisions, butalso the adequacy of the resulting representation ofvulnerability. This could be performed by asking thelocal panel to “draw” a map of social vulnerabilityfor their study area, which could then be comparedto various approaches for index creation to aid in theselection of an “optimal” approach. If this were re-peated for several study areas, it may be possible toreach conclusions not only about the sensitivity of thealgorithm, but also to make recommendations on op-timal approaches to index construction.

Our discussion on the importance of expert judg-ment in the creation and analysis of social vulnerabil-ity indicators also provides an opportunity for broaderreflections on the ties between qualitative and quan-titative approaches to the analysis of social vulnera-bility. Oftentimes, these two approaches to researchare viewed as contradictory, but this obscures the im-portant interplay between the two methodologies.

The creation of reliable quantitative indices ofsocial vulnerability provides a meaningful tool thatprovides a comparison among places, which can assistin the allocation of preparedness resources and theselective targeting of areas that may need additionalhelp in the aftermath of a natural or human-induceddisaster. When mapped, the quantitative social vul-nerability provides a useful mechanism for conveyinginformation to nonspecialists such as policymakers,and allows them to visualize differences between thecounties or between the neighborhoods within cities.By their very nature, however, indices are summarycharacterizations that may not always provide a com-

plete understanding of the driving forces underlyingsocial vulnerability or its distribution across the land-scape. We must be careful when employing numericalvulnerability indices to realistically represent the un-derlying vulnerability, and not other hidden or relatedphenomena. We must also ensure that when applyingthese measures, any mitigation strategies will in factdecrease vulnerability (theoretically and practically),not just the value of the vulnerability index.

Where quantitative measures are weak, qualita-tive measures are strong. In-depth qualitative analy-sis, such as case studies, often proves indispensable inproviding the context necessary for successful appli-cation of quantitative index constructions. As high-lighted in the analysis above, the context in whichquantitative indices are applied influences the waythey behave. Important variables may be overlookedin practice if knowledge gained through qualitativeanalyses is not considered. And, in-depth case stud-ies provide better information on the actual mannerin which vulnerability manifests itself within a studyarea, providing information critical to the design ofappropriate preparedness, response, and mitigationstrategies.

Rather than solely informing quantitative analy-sis, however, qualitative studies are informed by themas well. The quick, broad assessments of vulnerabilityprovided by quantitative indices are useful guides forthe selection of study areas in which more intensive,qualitative analyses may be conducted.

Our analysis represents a first step toward un-derstanding the sensitivity of the social vulnerabilitymetric. We have demonstrated that the algorithm isrobust to minor changes in variable composition andto changes in scale, but is sensitive to changes in itsquantitative construction. In light of this sensitivity,we also have highlighted the need for expert guid-ance when constructing the index. The SoVI providesan understanding of the spatial dimensions of socialvulnerability in diverse settings. Once a region’s mostvulnerable subareas are delineated in a systematicfashion, case-study research on the local drivers pro-ducing the pattern of vulnerability can begin, leadingto reduced social vulnerabilities, and improved localresilience to environmental threats where and when-ever they occur.

ACKNOWLEDGMENTS

This research was supported through a grant fromthe National Science Foundation (CMS 0433158), aspart of the Human and Social Dynamics Program.


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